In the context of the linear regression model, Shively (1988) has constructed a point optimal test for constant coefficients against the alternative of return to normalcy coefficients. This paper considers alternative methods for the choice of values of the unknown parameters required to conduct the test. These alternatives are based on Cox and Hinkley's (1974, p.102) idea of maximising some weighted average of powers. The paper explores the use of some simple weighting schemes and demonstrates by an empirical power comparison the usefulness of maximising some weighted average of powers in solving this testing problem.